On a free group of transformations defined by an automaton

We prove that three automorphisms of the rooted binary tree defined by a certain 3-state automaton generate a free non-Abelian group of rank 3. Both authors are supported by the NSF grants DMS-0308985 and DMS-0456185. Yaroslav Vorobets is supported by a Clay Research Scholarship.     

Pseudoparabolic variational inequalities without initial conditions

We consider a pseudoparabolic variational inequality in a cylindrical domain semibounded in a variable t. Under certain conditions imposed on the coefficients of the inequality, we prove theorems on the unique existence of a solution for a class of functions with exponential growth as t → ∞. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 7, pp. 919–929, July, 1998.     

Integral representation of a solution to the Stokes–Darcy problem

With methods of potential theory, we develop a representation of a solution of the coupled Stokes–Darcy model in a Lipschitz domain for boundary data in H^?1/2. Copyright © 2014 John Wiley & Sons, Ltd.     

A Versatile Solid-Phase Approach to the Synthesis of Oligonucleotide Conjugates with Biodegradable Hydrazone Linker

One of the ways to efficiently deliver various drugs, including therapeutic nucleic acids, into the cells is conjugating them with different transport ligands via labile or stable bonds. A convenient solid-phase approach for the synthesis of 5′-conjugates of oligonucleotides with biodegradable pH-sensitive hydrazone covalent bonds is proposed in this article. The approach relies on introducing a hydrazide of the ligand under aqueous/organic media to a fully protected support-bound oligonucleotide containing aldehyde function at the 5′-end. We demonstrated the proof-of-principle of this approach by synthesizing 5′-lipophilic (e.g., cholesterol and α-tocopherol) conjugates of modified siRNA and non-coding RNAs imported into mitochondria (antireplicative RNAs and guide RNAs for Mito-CRISPR/system). The developed method has the potential to be extended for the synthesis of pH-sensitive conjugates of oligonucleotides of different types (ribo-, deoxyribo-, 2′-O-methylribo-, and others) with ligands of different nature.     

Molecular and conformational properties of comb-like polymers with ionically bound side chains studied in organic solvent

Conformational and dynamo-optical properties of a homologous series of poly(cetyltrimethylammonium 2-acrylamido-2-methylpropane sulfonates) with molecular masses ranging from 80 to 700?kDa were studied in chloroform solutions by viscometry, dynamic light scattering, sedimentation, and flow birefringence. The Mark–Kuhn–Houwink Equations for this polymer in chloroform were obtained; the values of hydrodynamic diameter and the Kuhn segment length as well as the value of intrinsic anisotropy of polarizability of the monomer unit were defined.     

Correction to: Lithium ion conductivity of solid solutions based on Li8ZrO6

Journal of Solid State Electrochemistry - Lithium ion conductivity of lithium hexaoxozirconate Li8ZrO6 doped by Mg2+, Sr2+, Nb5+, V5+, and Ce4+ cations was studied using impedance spectroscopy. The...     

CeO2/Pd Nanoparticles Incorporated Fly Ash Zeolite: An Efficient and Recyclable Catalyst for Csp2-Csp2 Bond Formation Reactions

The catalytic activity of CeO₂ and palladium nanoparticles supported fly ash zeolite (CeO₂/Pd@FAZ) for C_sp²-C_sp² bond formation was studied. CeO₂/Pd@FAZ was characterized by FTIR, XRD, EDAX and TEM studies. In the Suzuki-Miyauracross-coupling reaction, biphenyl derivatives with excellent yields were obtained, and the reaction conditions were optimized. The catalytic activity was explored using a wide variety of diversely substituted aryl bromides and chlorides with aryl boronic acid under optimized reaction conditions. The recyclability of the catalyst was established for three cycles, with the conversion rate from 99 to 40%, which gained the advantage of heterogeneous catalysis.     

Evaluation of pigments from methanolic extract of Tagetes erecta and Beta vulgaris as antioxidant and antibacterial agent

The Total Phenolic Content (TPC), antioxidant and antibacterial activities of methanolic extract of Marigold flower (MF) (Tagetes erecta) and Beet root (BR) (Beta vulgaris) were examined. The present work reveals that MF contained greater amount of TPC (42.5 mg/g GAE) as compared to BR (39.4 mg/g GAE). Methanolic extract of MF exhibited excellent DPPH free radical scavenging power (IC₅₀ 0.0716 mg/mL) and reducing power at 1 mg/mL concentration. Similar results have been obtained in FTC and TBA method. The results of antibacterial test indicated that the methanolic extract of MF and BR is significantly effective against both type of Gram-negative (Escherichia coli, Shigella dysenteriae) and Gram-positive (Bacillus subtilis, Staphylococcus aureus) bacterial strains. Therefore, the present study suggests that the Marigold and BR are promising source of herbal medicinal products with noteworthy antioxidant and antibacterial activity.     

Boundary-Value Problem for Weakly Nonlinear Hyperbolic Equations with Variable Coefficients

We establish conditions for the unique solvability of a boundary-value problem for a weakly nonlinear hyperbolic equation of order 2n, n > (3p + 1)/2, with coefficients dependent on the space coordinates and data given on the entire boundary of a cylindric domain . The investigation of this problem is connected with the problem of small denominators.     

Crystallization and stereocomplexation behavior of poly(D‐ and L‐lactide)‐b‐poly(N,N‐dimethylamino‐2‐ethyl methacrylate) block copolymers

The thermal properties, crystallization, and morphology of amphiphilic poly(D ‐lactide)‐b‐poly(N,N‐dimethylamino‐2‐ethyl methacrylate) (PDLA‐b‐PDMAEMA) and poly (L ‐lactide)‐b‐poly(N,N‐dimethylamino‐2‐ethyl methacrylate) (PLLA‐b‐PDMAEMA) copolymers were studied and compared to those of the corresponding poly(lactide) homopolymers. Additionally, stereocomplexation of these copolymers was studied. The crystallization kinetics of the PLA blocks was retarded by the presence of the PDMAEMA block. The studied copolymers were found to be miscible in the melt and the glassy state. The Avrami theory was able to predict the entire crystallization range of the PLA isothermal overall crystallization. The melting points of PLDA/PLLA and PLA/PLA‐b‐PDMAEMA stereocomplexes were higher than those formed by copolymer mixtures. This indicates that the PDMAEMA block is influencing the stability of the stereocomplex structures. For the low molecular weight samples, the stereocomplexes particles exhibited a conventional disk‐shape structure and, for high molecular weight samples, the particles displayed unusual star‐like shape morphology. © 2011 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 49: 1397–1409, 2011